Question

In a plantation drive, 576 trees are to be planted in a plot so that the number of trees in each row equals the total number of rows. The number of rows is .

Answer 1

The condition is to plant a number of trees in each row equal to the total number of rows.
$\therefore \text{Number of rows}=\text{Number of columns}$

$\text{Total number of trees}=\text{Number of rows}\times \text{Number of columns}=\text{Number of rows}\times \text{Number of rows}$

$\Rightarrow \text{Total number of trees}={\text{Number of rows}}^2$

$\Rightarrow \sqrt{\text{Total number of trees}}=\text{Number of rows}$

$\Rightarrow \text{Number of rows}=\sqrt{576}$

Using prime factorization,
$576=2^6\times 3^2$
$\Rightarrow 576=(2^3\times 3{)}^2$
$\Rightarrow \sqrt{576}=24$

$\therefore$ Number of rows $=24$